Definition 23 ([1]}) 

Let \(\mathbf {H}\)  be a \(p\) -uniform hypergraph having \(n\)  vertices and \(m\)  hyperedges.
The free structure \(\mathbb {F}_{{{M}}}(\mathbf {H})\)  of a linear minion \({{M}}\)  generated by \(\mathbf {H}\)  is the (potentially infinite) \(p\) -uniform hypergraph on the vertex set \(V(\mathbb {F}_{{{M}}}(\mathbf {H}))={{M}}^{(n)}\)  whose hyperedges are defined as follows: Given \(M_1,\dots ,M_p\in {{M}}^{(n)}\) , the tuple \((M_1,\dots ,M_p)\)  belongs to \(E(\mathbb {F}_{{{M}}}(\mathbf {H}))\)  if and only if there exists some \(Q\in {{M}}^{(m)}\)  such that \(M_i=Q_{/\pi _i}\)  for each \(i\in [p]\) , where \(\pi _i:E(\mathbf {H})\rightarrow V(\mathbf {H})\)  maps a hyperedge \(\mathbf {h}\)  to its \(i\) -th entry \(h_i\) .

